Final answer:
When a positive integer n is divided by 3, and the remainder is 2, the possible values of n are 2, 5, 8, 11, 14, 17, and so on.
Step-by-step explanation:
When a positive integer n is divided by 3, and the remainder is 2, we can write it as n = 3k + 2, where k is a non-negative integer. By substituting different values of k, we can find the possible values of n.
For example, when k = 0, n = 3(0) + 2 = 2. When k = 1, n = 3(1) + 2 = 5. When k = 2, n = 3(2) + 2 = 8.
If n is a positive integer and when n is divided by 3, the remainder is 2, the values of n can be represented by the expression 3k + 2 where k is an integer. This is because any integer n, when divided by another integer, can be expressed in the form n = dividend × divisor + remainder.
Therefore, n can be 2, 5, 8, 11, 14, and so on, following the pattern that every subsequent number is 3 more than the previous one. In simpler terms, n belongs to the set of numbers {2, 5, 8, 11, ...} where these numbers are all 2 more than a multiple of 3.
Therefore, the possible values of n are 2, 5, 8, 11, 14, 17, and so on.